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On the reflexion of surface waves by a submerged circular cylinder

Published online by Cambridge University Press:  24 October 2008

W. R. Dean
W. R. Dean
Affiliation:
Trinity CollegeCambridge
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Extract

1. In a recent paper (1) the reflexion of surface waves by a submerged plane barrier has been considered, and it has been shown that there is a reflected wave of finite amplitude at a great distance from the barrier, so that the coefficient of reflexion (the ratio of the amplitudes, at a great distance from the barrier, of the reflected and incident waves) is finite. In this paper it is shown that in the case of reflexion by a submerged circular cylinder, the coefficient of reflexion is zero, with the result that the only effect of the obstacle at a great distance is that there is a phase-difference between the incident and transmitted waves, their amplitudes being the same. Only one case has been worked out in detail numerically, and the method employed is such that the condition that the section of the cylinder must be a stream-line has been satisfied only to an approximation; it is, however, shown that the coefficient of reflexion is zero in the general case.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 4 , October 1948 , pp. 483 - 491
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Dean, W. R.Proc. Cambridge Phil. Soc. 41 (1945), 231.CrossRefGoogle Scholar
(2) The first integral is given in Whittaker, and Watson, , Modern analysis (2nd ed., Cambridge, 1915), p. 116; in the formula for the second, the principal value is to be taken of the integral with respect to y. The function Ei(x) is tabulated in B.A. Mathematical Tables, vol. 1 (London, 1931).Google Scholar